An EDG Method for Distributed Optimal Control of Elliptic PDEs

TL;DR

This paper introduces an EDG method for solving distributed optimal control problems governed by elliptic PDEs, providing theoretical error estimates and numerical validation.

Contribution

The paper develops an embedded discontinuous Galerkin method with optimal error estimates for elliptic PDE control problems, advancing numerical approximation techniques.

Findings

Optimal a priori error estimates for state and control.

Numerical experiments confirm theoretical error bounds.

Method effectively approximates solutions to elliptic PDE control problems.

Abstract

We consider a distributed optimal control problem governed by an elliptic PDE, and propose an embedded discontinuous Galerkin (EDG) method to approximate the solution. We derive optimal a priori error estimates for the state, dual state, the optimal control, and suboptimal estimates for the fluxes. We present numerical experiments to confirm our theoretical results.